Wrong. Jesus Christ never taught that.
You're a funny guy. Of course Christ didn't exalt Himself. God the Father anointed Him as the High Priest. he was also glorified as such by the Apostles. Peter did,
1Pe 2:3-7 (3) If so be ye have tasted that the Lord is gracious. (4) To whom coming, as unto a living stone, disallowed indeed of men, but chosen of God, and precious, (5) Ye also, as lively stones, are built up a spiritual house, an holy priesthood, to offer up spiritual sacrifices, acceptable to God by Jesus Christ. (6) Wherefore also it is contained in the scripture, Behold, I lay in Zion a chief corner stone, elect, precious: and he that believeth on him shall not be confounded. (7) Unto you therefore which believe he is precious: but unto them which be disobedient, the stone which the builders disallowed, the same is made the head of the corner,
Also in Hebrews
Heb 5:1-6 (1) For every high priest taken from among men is ordained for men in things pertaining to God, that he may offer both gifts and sacrifices for sins: (2) Who can have compassion on the ignorant, and on them that are out of the way; for that he himself also is compassed with infirmity. (3) And by reason hereof he ought, as for the people, so also for himself, to offer for sins. (4) And no man taketh this honor unto himself, but he that is called of God, as was Aaron. (5) So also Christ glorified not himself to be made a high priest; but he that said unto him, Thou art my Son, today have I begotten thee. (6) As he saith also in another place, Thou art a priest forever after the order of Melchizedek.
Heb 7:25 (25) Wherefore he is able also to save them to the uttermost that come unto God by him, seeing he ever liveth to make intercession for them.